Question

For the following A.P.s, write the first term and the common difference.
(i) 3, 1, – 1, – 3 …
(ii) -5, – 1, 3, 7 …
(iii) 1/3, 5/3, 9/3, 13/3 ….​

Answer 1

S O L U T I O N :

(I). 3, 1, – 1, – 3 …

→ First term (a) = 3

$\checkmark$ a = 3

→ Common difference (d) = Second term - First term

→ d = t2 - t1

→ d = 1 - 3

$\checkmark$ d = -2

(II). -5, – 1, 3, 7 …

→ First term (a) = -5

$\checkmark$ a = -5

→ Common difference (d) = Second term - First term

→ d = t2 - t1

→ d = -1 - (-5)

$\checkmark$ d = 4

(III). 1/3, 5/3, 9/3, 13/3 ….

→ First term (a) = 1/3

$\checkmark$ a = 1/3

→ Common difference (d) = Second term - First term

→ d = t2 - t1

→ d = 5/3 - 1/3

$\checkmark$ d = 4/3

For information,

• a_n = a + (n - 1)d
• S_n = n/2 × (2a + (n - 1)d)
• S_n = n/2 × (a + l)